RSS feeds
ÐóññêèéEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1992

 / 

February

←  →

Reviews of topical problems


The Skyrme model and strong interactions (On the 30th anniversary of the creation of the Skyrme model)

 a,  b,  b
a Joint Institute for Nuclear Research, 6 Joliot-Curie Str., Dubna, Moscow Region, 141980, Russian Federation
b Department of Experimental Physics, Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation

The review summarizes the development of Skyrme's soliton approach to the description of baryon structure. In contrast to existing literature on this subject, the principal attention is devoted not to the pragmatic aspects of the model, but rather to its initial ideas, to its deep topological content and to such subtle problems as the existence of solutions, the attainability of the absolute energy minimum based on the hedgehog ansatz, and so on. It is exactly these features of the Skyrme approach that are, in the authors' opinion, the main advantages compared to other schemes used in strong-interaction physics. The material assembled in the review will, first, enable the reader to gain a deeper understanding of the structure and special features of the Skyrme model and, second, will serve as an adequate base for further modifications and for development of more realistic scenarios of processes in low-energy QCD, the need for which is beyond any doubt.

Fulltext pdf (1.6 MB)
Fulltext is also available at DOI: 10.1070/PU1992v035n02ABEH002214
PACS: 11.10.Lm, 12.38.−t, 14.20.−c, 11.30.Rd, 12.39.Ba, 21.65.+f (all)
DOI: 10.1070/PU1992v035n02ABEH002214
URL: https://ufn.ru/en/articles/1992/2/a/
Citation: Makhan’kov V G, Rybakov Yu P, Sanyuk V I "The Skyrme model and strong interactions (On the 30th anniversary of the creation of the Skyrme model)" Sov. Phys. Usp. 35 (2) 55–84 (1992)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Ìàõàíüêîâ Â Ã, Ðûáàêîâ Þ Ï, Ñàíþê Â È «Ìîäåëü Ñêèðìà è ñèëüíûå âçàèìîäåéñòâèÿ (Ê 30-ëåòèþ ñîçäàíèÿ ìîäåëè Ñêèðìà)» ÓÔÍ 162 (2) 1–61 (1992); DOI: 10.3367/UFNr.0162.199202a.0001

References (132) ↓ Cited by (18) Similar articles (20)

  1. Skyrme T H R Proc. R. Soc. London A 226 521 (1954)
  2. Skyrme T H R Proc. R. Soc. London A 230 277 (1955)
  3. Skyrme T H R Nuovo Cimento Suppl. 4 749 (1956)
  4. Skyrme T H R Proc. R. Soc. London A 247 260 (1958)
  5. Skyrme T H R Proc. R. Soc. London A 252 236 (1959)
  6. Skyrme T H R Proc. R. Soc. A 262 237 (1961)
  7. Pauli V. Mezonnaya Teoriya Yadernykh Sil (M.: IL, 1947)
  8. Faddeev L.D. Pis’ma ZhETF 21 141 (1975)
  9. Skyrme T H R Int. J. Mod. Phys. A 3 2745 (1988)
  10. Thomson W Proc. R. Soc. Edinburgh 6 94 (1869)
  11. Filippov A.T. Mnogolikii Soliton (M.: Nauka, 1986)
  12. Makhan’kov V.G., Rybakov Yu.P., Sanyuk V.I. Model’ Skirma i Solitony v Fizike Adronov (Lektsii dlya molodykh uchenykh. Vyp. 55. R489568) (Dubna: OIYaI, 1989)
  13. Pais A Physica 19 869 (1953); Pais A Proc. Natl. Acad. Sci. U.S.A. 40 484 (1954)
  14. Schwinger J Phys. Rev. 104 1164 (1956); Schwinger J Ann. Phys. New York 2 407 (1957)
  15. Feynman R, Gell-Mann M Phys. Rev. 109 1067 (1958)
  16. De Al’faro V., Fubini S., Furlan G., Rosetti K. Toki v Fizike Adronov (M.: Mir, 1976) p. 215
  17. Weinberg S Phys. Rev. 166 1568 (1968)
  18. Skott E., Chu F., Mak-Laflin D. Skott E. Volny v Aktivnykh Nelineinykh Sredakh v Prilozhenii k Elektronike (M.: Sov. radio, 1977) p. 215
  19. Zakharov V.E., Manakov S.V., Novikov S.P., Pitaevskii L.P. Teoriya Solitonov: Metod Obratnoi Zadachi (M.: Nauka, 1980)
  20. Radzharaman R. Solitony i Instantony v Kvantovoi Teorii Polya (M.: Mir, 1985)
  21. Ablovitts M., Segur X. Solitony i Metod Obratnoi Zadachi (M.: Mir, 1987)
  22. Dodd R., Eilbek Dzh., Gibbon Dzh., Morris X. Solitony i Nelineinye Volnovye Uravneniya (M.: Mir, 1988)
  23. Perring J K, Skyrme T H R Nucl. Phys. 31 550 (1962)
  24. Zabusky N J, Kruscal M D Phys. Rev. Lett. 15 240 (1965)
  25. Coleman S Phys. Rev. D 11 2088 (1975)
  26. Finkelstein D, Misner Ch Ann. Physics 6 230 (1959)
  27. Finkelstein D J. Math. Phys. 7 1218 (1966)
  28. von Westenholz C Ann. Inst. Henri Poincare A 30 353 (1979)
  29. Ol’shanetskii M.A. Usp. Fiz. Nauk 136 421 (1982); Ol’shanetskii M A Sov. Phys. Usp. 25 123 (1982)
  30. Shvarts A.S. Kvantovaya Teoriya Polya i Topologiya (M.: Nauka, 1989)
  31. Dubrovin B.A., Novikov S.P., Fomenko A.T. Sovremennaya Geometriya: Metody i Prilozheniya (M.: Nauka, 1986)
  32. Skyrme T H R Proc. R. Soc. London A 260 127 (1961)
  33. Skyrme T H R Nucl. Phys. 31 556 (1962)
  34. Sanyuk B.I. Problemy fiziki vysokikh energii i teorii polya. Trudy XI seminara (M.: Nauka, 1989) p. 240; Sanyuk B.I. Problemy fiziki vysokikh energii i teorii polya. Trudy XII seminara (M.: Nauka, 1990) p. 254
  35. Sanyuk V I IVth International Workshop On "Solitons And Applications" (Eds V G Mahankov, V K Fedyanin, O K Pashaev) (Singapore: World Scientific, 1990) p. 374
  36. Skyrme T H R J. Math. Phys. 12 1755 (1971)
  37. Rybakov Yu.P. Problemy Teorii Gravitatsii i Elementarnykh Chastits. Vyp. 14 (M.: Energoizdat, 1984) p. 161
  38. Rybakov Yu P, Chakrabarti S Int. J. Theor. Phys. 23 325 (1984)
  39. Hobart R H Proc. Phys. Soc. London 82 201 (1963)
  40. Derrick G H J. Math. Phys. 5 1252 (1964)
  41. Faddeev L. D. Nelokal’nye, Nelineinye i Nerenormiruemye Teorii Polya (D2-9788) (Dubna: OIYaI, 1976) p. 207
  42. Palais R Commun. Math. Phys. 69 19 (1979)
  43. Ladyzhenskaya O.A., Kapitanskii L.V. Zap. Nauchnykh Seminarov LOMI 127 (15) 84 (1983)
  44. Rybakov Yu.P. Problemy Teorii Gravitatsii i Elementarnykh Chastits. Vyp. 10 (M.: Atomizdat, 1979) p. 194
  45. Romanov V.P., Frolov I.V., Shvarts A.S. Teor. Mat. Fiz. 37 305 (1978); Rybakov Yu P, Sanyuk V I The Niels Bohr Inst. preprint NBIHE8149 (Copenhagen: The Niels Bohr Inst., 1981)
  46. Rybakov Yu.P. Problemy Teorii Gravitatsii i Elementarnykh Chastits. Vyp. 13 (M.: Energoatomizdat, 1982) p. 187
  47. Kozhevnikov I.R., Rybakov Yu.P., Fomin M.B. Teor. Mat. Fiz. 75 353 (1988)
  48. Nisichenko V.P. Avtoreferat dissertatsii... kand. fiz.mat. nauk (M.: UDN, 1981)
  49. Bogomol’nyi E.B., Fateev V.A. Yad. Fiz. 37 228 (1983)
  50. Atiyah M F, Manton N S Phys. Lett. A 228 438 (1989)
  51. Akhiezer N.E., Glazman I.M. Teoriya Lineinykh Operatorov v Gil’bertovom Prostranstve (M.: Nauka, 1966)
  52. Lyusternik L.A., Sobolev V.I. Elementy Funktsional’nogo Analiza (M.: Nauka, 1965)
  53. Sobolev S.L. Nekotorye Primeneniya Funktsional’nogo Analiza v Matematicheskoi Fizike (Novosibirsk: Izdvo SO AN SSSR, 1962)
  54. Rybakov Yu.P. Problemy fiziki vysokikh energii i teorii polya. Trudy X seminara (M.: Nauka, 1988) p. 349
  55. Kopeliovich V.B., Shtern B.E. Pis’ma ZhETF 45 165 (1987)
  56. Verbaarshot J J M Phys. Lett. B 195 235 (1987)
  57. Braaten E, Townsend S, Carson L Phys. Lett. B 235 147 (1990)
  58. Kudriavtsev A E, Martemyanov B V Preprint ITEP-9 (Moscow: ITEP, 1985)
  59. Braaten E Solitons In Nuclear And Elementary Particles Physics (Eds A Chodos, E Hadjimichael, C Tze) (Singapore: World Scientific, 1984) p. 57; Blaizot J P, Ripka G Phys. Rev. C 38 1556 (1988)
  60. Holzwarth G, Schwesinger B Rep. Prog. Phys. 49 825 (1986)
  61. Vakulenko A.F., Kapitanskii L.V. Dokl. Akad. Nauk SSSR 246 840 (1979)
  62. Kundu A, Rybakov Yu P J. Phys. A 15 269 (1982)
  63. Gipson J M, Tze H C Nucl. Phys. B 183 524 (1983)
  64. Fujii K, Otsuki S, Toyoda F Prog. Theor. Phys. 73 1287 (1985)
  65. t’Hooft G Nucl. Phys. B 72 461 (1974)
  66. Slavnov A.A. Teor. Mat. Fiz. 51 307 (1982); Slavnov A.A. Teor. Mat. Fiz. 57 4 (1983)
  67. Witten E Solitons In Nuclear And Elementary Particles Physics (Eds A Chodos, E Hadjimichael, C Tze) (Singapore: World Scientific, 1984) p. 306
  68. Berlin T H, Kac M Phys. Rev. 86 821 (1952)
  69. Sukhatme U, Imbo T Phys. Rev. D 28 418 (1983)
  70. Witten E Nucl. Phys. B 160 57 (1979); Witten E Phys. Today 33 ((7)) 38 (1980)
  71. Balalchandran A P, Nair V P, Rajeev S G, Stern A Phys. Rev. Lett. 49 1124 (1982); Balalchandran A P, Nair V P, Rajeev S G, Stern A Phys. Rev. Lett. 50 1630 (1983); Balalchandran A P, Nair V P, Rajeev S G, Stern A Phys. Rev. D 27 1153 (1983); Balalchandran A P, Nair V P, Rajeev S G, Stern A Phys. Rev. D 27 2772 (1983)
  72. Balachandran A P High Energy Physics’85 Vol. 1 (Eds M J Bowick, F Gursey) (Singapore: World Scientific, 1986) p. 1
  73. Goldstone J, Wilczek F Phys. Rev. Lett. 47 986 (1981)
  74. Kahana S, Ripka G, Soni V Nucl. Phys. A 415 351 (1984)
  75. Kahana S, Ripka G Nucl. Phys. A 429 426 (1984)
  76. Shuryak E V Phys. Rep. 115 151 (1985)
  77. Diakonov D I Skyrmions And Anomalies (Eds M Jezabek, M Praszalowicz) (Singapore: World Scientific, 1987) p. 27
  78. Adler S Phys. Rev. 177 2426 (1969); Bell J S, Jackiw R Nuovo Cimento 60 147 (1969); Bardeen W A Phys. Rev. 184 1848 (1969)
  79. Fomin P I, Gusynin V P, Miranski V A, Sitenko Yu A Riv. Nuovo Cimento 6 1 (1984)
  80. Wess J, Zumino B Phys. Lett. B 37 95 (1971)
  81. Karchev N.I., Slavnov A.A. Teor. Mat. Fiz. 65 192 (1985)
  82. Slavnov A.A., Faddeev L.D. Vvedenie v Kvantovuyu Teoriyu Kalibrovochnykh Polei (M.: Nauka, 1988)
  83. Andrianov A A, Novozhilov Yu Phys. Lett. B 153 422 (1985); Andrianov A A Phys. Lett. B 157 425 (1985)
  84. Andrianov A A, Andrianov V A, Novozhilov V Yu, Novozhilov Yu V Lett. Math. Phys. 11 217 (1986); Andrianov A.A., Andrianov V.A., Novozhilov V.Yu., Novozhilov Yu.V. Teor. Mat. Fiz. 70 63 (1987)
  85. Andrianov A A, Bonora L Nucl. Phys. B 232 232 (1984); Andrianov A A, Bonora L Nucl. Phys. B 232 247 (1984)
  86. Chodos A, Thorn C B Phys. Rev. D 12 2733 (1975)
  87. Rho M, Goldhaber A S, Brown G E Phys. Rev. Lett. 51 747 (1983); Goldstone J, Jaffe R L Phys. Rev. Lett. 51 1518 (1983); Brown G E, Rho M Phys. Rev. Lett. 82 177 (1979)
  88. Kaymakcalan Ö, Rajeev S, Schechter J Phys. Rev. D 30 594 (1984); Kaymakcalan Ö, Schechter J Phys. Rev. D 31 1109 (1985); Meissner U-G, Zahed I Phys. Rev. Lett. 56 1035 (1986)
  89. Nadkarni S, Nielsen H B, Zahed I Nucl. Phys. B 253 308 (1985); Nadkarni S, Nielsen H B, Zahed I Nucl. Phys. B 263 1 (1986); Nadkarni S, Nielsen H B, Zahed I Nucl. Phys. B 263 23 (1986)
  90. Nielsen H B Skyrmions And Anomalies (Eds M Jezabek, M Praszalowicz) (Singapore: World Scientific, 1987) p. 277
  91. Vepstas L, Jackson A D, Goldhaber A S Phys. Lett. B 140 280 (1984); Wust E, Vepstas L, Jackson A D Phys. Lett. B 173 217 (1986)
  92. Vinitskii S.I., Debrov V.I., Dubovik V.M., Markovski B.L., Stepanovskii Yu.P. Usp. Fiz. Nauk 160 1 (1990); Vinitskii S I, Debrov V L, Dubovnik V M, Markovski B L, Stepanovskii Yu P Sov. Phys. Usp. 33 403 (1990)
  93. Balachandran A P, Gomm H, Sorkin R D Nucl. Phys. B 281 573 (1987)
  94. Mackenzie R, Wilczek F Int. J. Mod. Phys. A 3 2827 (1988)
  95. Markovski B, Vinitsky S I (Eds) Topological Phases In Quantum Physics (Singapore: World Scientific, 1989)
  96. Jezabek M, Praszalowicz M (Eds) Skyrmions And Anomalies (Singapore: World Scientific, 1987)
  97. Finkelstein D, Rubinstein J J. Math. Phys. 9 1762 (1968)
  98. Williams J J. Math. Phys. 11 2611 (1970)
  99. Schwarz A S Mod. Phys. Lett. A 4 403 (1989)
  100. Ravenel D, Zee A Commun. Math. Phys. 98 239 (1985)
  101. Zaccaria F., SudarshanE. C.G., Nielson J. S., Mukunda N., Marmo G., Balacliandran A.P. Phys. Rev. D 27 2327 (1983)
  102. Balacliandran A.P., Marmo G., Skagerstam B.S., Stern A. Gauge Symmetries And Fibre Bundles: Applications To Particle Dynamics (Lecture Notes in Physics) Vol. 188 (Berlin: Springer-Verlag, 1983)
  103. Balacliandran A.P., Nair V.P., Trahern C.G. Phys. Rev. D 27 1369 (1983)
  104. Berry M Proc. R. Soc. London A 392 45 (1984)
  105. Aitchison I J R Acta Phys. Pol. B 18 207 (1987)
  106. Dzhekiv P. Usp. Fiz. Nauk 149 139 (1986)
  107. Sorkin R Commun. Math. Phys. 115 421 (1988)
  108. Balachandran A P Symposium On Anomalies, Geometry And Topology (Eds W A Bardeen, A R White) (Singapore: World Scientific, 1985) p. 472
  109. E.M. Collaboration (Aschman J et al.) Phys. Lett. B 206 364 (1988)
  110. Brodsky S.J., Ellis J., Karliner M. Phys. Lett. B 206 309 (1988)
  111. Kurihara T., Kanada H., Otofuji T., Saito S. Prog. Theor. Phys. 81 858 (1989); Nikolaev B.A., Tkachev O.G. Fiz. Elem. Chast. At. Yad. 21 1149 (1990)
  112. Diakonov D.I., Petrov V.Yu., Pobylitsa P.V. Nucl. Phys. B 306 809 (1988)
  113. Raider L. Kvantovaya Teoriya Polya (M.: Mir, 1987)
  114. Witten E Nucl. Phys. B 223 433 (1983)
  115. Bott R., Seely R. Commun. Math. Phys. 62 235 (1978)
  116. Diakonov D.I., Petrov F.Yu. Nucl. Phys. B 272 457 (1986)
  117. Wakamatsu M Phys. Rev. D 42 2427 (1990)
  118. Rybakov Yu.P. Problemy Teorii Gravitatsii i Elementarnykh Chastits. Vyp. 14 (M.: Energoatomizdat, 1984) p. 166
  119. Rybakov Yu.P., Sutantio V. Problemy Teorii Gravitatsii i Elementarnykh Chastits. Vyp. 15 (M.: Energoatomizdat, 1985) p. 137
  120. Jackson A., Jackson A.D., Pasquier V. Nucl. Phys. A 432 567 (1985)
  121. Zahedl., Brown G.E. Phys. Rep. 142 1 (1986); Meissner U-G, Zahed I. Adv. Nucl. Phys. 17 143 (1986); Meissner U-G Phys. Rep. 161 213 (1988)
  122. Vinh Moi. R. Orsay Preprint IPNO/TH 89-84 (1989)
  123. Kaiser N, Meissner U-G Phys. Lett. B 233 457 (1989)
  124. Nyman E.M., Riska D.O. Rep. Prog. Phys. 53 1137 (1990)
  125. Karliner M., Mattis M.P. Phys. Rev. D 34 1991 (1986)
  126. Braaten E., Cai D. Phys. Rev. Lett. 62 1243 (1989)
  127. Donohue J T Phys. Rev. D 41 2317 (1990)
  128. Pethick C J Nucl. Phys. A 434 587 (1985)
  129. Castillejo L., Jones P.S.J., Jackson A.D., Verbaarscfiot J.J.M., Jackson A. Nucl. Phys. A 501 801 (1989)
  130. Manton N S Commun. Math. Phys. 111 469 (1987)
  131. Manton N.S., Saniols T.M. J. Phys. A 23 3749 (1990)
  132. Rybakov Yu.P. Itogi Nauki i Tekhniki. Ser. "Klassicheskaya Teoriya Polya i Teoriya Gravitatsii. T.2. Gravitatsiya i Kosmologiya (M.: VINITI, 1991) p. 56
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions